scholarly journals Direct and indirect methods to optimize the muscular force response to a pulse train of electrical stimulation

2021 ◽  
Vol 71 ◽  
pp. 1-10
Author(s):  
Toufik Bakir ◽  
Bernard Bonnard ◽  
Loïc Bourdin ◽  
Jérémy Rouot
Keyword(s):  
Electrical Stimulation ◽  
Control Problem ◽  
Sampled Data ◽  
Force Response ◽  
Muscular Force ◽  
Direct Optimization ◽  
Indirect Methods ◽  
Data Control ◽  
Direct And Indirect Methods ◽  
Sampling Times

Recent force-fatigue mathematical models in biomechanics [7] allow to predict the muscular force response to functional electrical stimulation (FES) and leads to the optimal control problem of maximizing the force. The stimulations are Dirac pulses and the control parameters are the pulses amplitudes and times of application, the number of pulses is physically limited and the model leads to a sampled data control problem. The aim of this article is to present and compare two methods. The first method is a direct optimization scheme where a further refined numerical discretization is applied on the dynamics. The second method is an indirect scheme: first-order Pontryagin type necessary conditions are derived and used to compute the optimal sampling times.

H∞ Robust State Feedback Sampled-Data Control of Interval Linear Systems

2020 ◽  
Author(s):  
Rafael M. Alves ◽  
André R. Fioravanti ◽  
Matheus Souza
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Hybrid Systems ◽  
Upper Bound ◽  
State Feedback ◽  
Data Systems ◽  
Sampled Data ◽  
Data Control ◽  
Interval Linear ◽  
Interval Linear Systems

In this paper, we address the H∞ control problem for uncertain sampled-data systems rewritten as hybrid systems. The conditions proposed are formulated as intervals to ensure stability and design controllers that guarantee an upper bound for an associated H∞ norm. A numerical example points out the main features of the proposed method.

Sampled-Data Control of Large-Scale Fuzzy Interconnected Systems

2017 ◽  
pp. 84-126
Keyword(s):  
Control Problem ◽  
Large Scale ◽  
Interconnected Systems ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control ◽  
Small Gain ◽  
Data Controller ◽  
Wirtinger’S Inequality

This chapter aims to study the sampled-data stabilization for large-scale fuzzy interconnected systems. We use two approaches to design the decentralized fuzzy sampled-data controller: Wirtinger's inequality and scaled small gain (SSG) theorem. Our aim is to derive the co-design consisting of the controller gains and sampled period in terms of a set of LMIs. Also, we consider the distributed sampled-data control problem, where the sampling periods among all subsystems may be different, and the actuator in each subsystem is time-driven. Finally, two simulation examples are provided to validate the advantage of the proposed methods.

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